B There are 20 people who wish to run for an officer position of the organizatio
ID: 3320962 • Letter: B
Question
B There are 20 people who wish to run for an officer position of the organization People Opposed to Fairness and Decency. The available slots are President, Secret ary, and Controller. How many ways could the slots be filled: 1) if no one can occupy more than one position? 2) if one person can occupy at most two positions? (In neither case can slots go unfilled). Finally, 3) how would things change if the organization decides to change its governance model to a junta, where there are simply three people who jointly take on al responsibilities, with no distinction bet ween them? That is, how many ways could a 3-person junta be selected from the 20 people?Explanation / Answer
Given, there are 20 people. There are 3 distinct posts namely President, Secretary and Controller
1) If no one can occupy more than one position.(Given, slots cannot go unfilled)
Since the positions are distinct, we use permutations.
For the first post there are 20 options.
For the second post there are 19 options.( one from 20 has already been chosen for first post)
For the third post there are 18 options.(2 have already been chosen from the 20 for first and second post)
Total number of ways=20*19*18=6840
2) If one person can occupy atmost 2 positions (Given, slots cannot go unfilled)
Since the positions are distinct, we use permutations.
For the first post there are 20 options.
For the second post there are 20 options(one person can occupy atmost 2 positions)
For the third post there are 19 options(one person out of 20 has occupied first 2 positions)
Total number of ways=20*20*19=7600
3) Number of ways 3-persons can be selected from 20.
This is a case of using combinations since the positions are not distinct
C(20,3)=20!/(3!)(17!)=1140
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